This will be from a mx perspective because it's what I'm most familiar with but the principles should largely be the same for ops.
PAA - Primary Aircraft Authorized. This is the number of aircraft that you are assigned on paper for the execution of your mission. This is what you get manning, equipment, and money against. Think of it as a "UMD" for aircraft.
BAA - Backup Aircraft Authorized. This is the number of aircraft that you are assigned on paper to help plug in the holes that will inevitably exist in your PAA because of stuff like phase/ISO, depot, etc. Again, this is an authorization so it's a number on paper, not iron.
PAI - Primary Aircraft Inventory. This is the number of aircraft you've got on the ramp up to your PAA (your PAI can never exceed your PAA).
BAI - Backup Aircraft Inventory. This is the number of any aircraft you have on the ramp above and beyond your PAA up to your BAA (similar to above, your BAI cannot exceed your BAA).
AR - Attrition Reserve. This is the number of aircraft, AF wide, that the AF determines it needs to procure above and beyond the PAA and BAA numbers to deal with expected attrition over the lifespan of the MDS. When a new MDS first comes online there won't be any AR, since they will be filling all the PAA and BAA authorizations. However, as the PAA and BAA becomes full, AR tails will start being distributed to bases AF wide. Not all MDS's will have an AR.
TAI - Total Active Inventory. Your PAI + BAI + AR (if any); the total amount of iron your unit possesses.
If I screwed any of that up, anyone feel free to jump in and correct me. AFI 16-402 is the relevant pub on the subject. Also with this subject you start to get into PPI codes...I'm not going to discuss those because that's a topic worthy of a BQZip powerpoint or a nsplayer dissertation, but AFI 21-103 is the relevant pub there if you want to get into it.
As for the rest of it, I'll just echo JS and bring up a couple of quick examples to hopefully hammer home the point...you talk about including "operational costs," and list mx and phase as examples of this. So that covers flightline maintainers and one backshop function, but what about the rest of the MXG? How do you factor in the costs of the other backshops? If I'm at a base with multiple MDS's, how do I divide up the cost of, say, AGE? None of the aircraft at that base can function without it, but what's a fair share distribution? Of course AGE flight is going to gain manning and equipment based on the PAA of the various MDS's, but there's several different ways you can twist that data. Step outside the MXG for a second to a favorite (sarcasm) subject of mine...supply. Maintenance would eventually come to a grinding halt if we had zero supply support for an extended period of time...so they should probably be included in the "operational costs" section right next to mx, right? But who gets included? Just the folks like COSO and MSL who work directly with the MXG? Do we take the amount of people/money/equipment that LRS Supply gains as a result of the PAA for that MDS that are assigned to that base? But can we stop at just the base? When I go MICAP, there's an entire worldwide network that is working to get (or not) me the part in a timely (or not so timely) fashion. How is that divided up across multiple MDS's?
Bottom line is that you have to draw a line somewhere, and where that line is drawn will influence the final results of your study.